Values of n such that a regular polygon with n sides can be formed by tying knots in a strip of paper. - Robert A. J. Matthews (rajm(AT)compuserve.com)

These polygons fill in many of the gaps left by the Greeks, who were restricted to compass and ruler. Specifically, they make possible construction of the regular 7-sided heptagon, 9-sided nonagon, 11-gon and 13-gon. The 14-gon becomes the first to be impossible by either ruler, compass or knotting.